1. Field of the Invention
The invention relates generally to optical communication systems and, more particularly, to transmission and reception of digital information bits encoded in duobinary, multilevel pulse-amplitude modulation optical signals which, for a given bit rate, have a narrow optical spectrum and low symbol rate, and enable the information bits to be recovered from the intensity of the received optical signal without potential error propagation.
2. Description of the Prior Art
It is well known that in optical communication systems conveying digital information, whether they transmit a single signal at a single carrier wavelength or transmit multiple signals at different carrier wavelengths (i.e., employ wavelength- division multiplexing), for a fixed bit rate per carrier wavelength, it is beneficial to design the transmitted signal to have a narrow optical spectrum and to use a long symbol interval. Throughout this patent, the term xe2x80x9coptical spectrumxe2x80x9d refers to the power spectral density of the transmitted optical electric field.
Furthermore, implementation of optical communication systems is simplified greatly if the transmitted signal is designed so that the transmitted information bits can be recovered at the receiver simply by extracting from the received optical signal an electrical signal proportional to the intensity of the received optical signal (i.e., the absolute square of the received optical electric field), and performing symbol-by-symbol decisions. Currently, almost all practical optical communication systems use direct detection, in which a photodetector generates a photocurrent proportional to the received optical signal intensity. It is also possible to extract an electrical signal proportional to the received optical signal intensity through other means, e.g., asynchronous homodyne or asynchronous heterodyne detection.
Single-sideband amplitude modulation is a traditional means to narrow the spectrum of a modulated signal by a factor of two, and involves modulation of a signal and its Hilbert transform onto quadrature carriers at the same carrier frequency. A few prior works have described single-sideband modulation of optical signals, but the single-sideband optical modulation schemes proposed to date are very difficult to implement in practice. Vestigial-sideband amplitude modulation is essentially an imperfect practical implementation of single-sideband amplitude modulation. Optical vestigial-sideband amplitude modulation can be implemented by first generating an amplitude-modulated optical signal and then filtering it with an optical filter having a sharp cutoff centered at the optical carrier frequency but, in practice, it is difficult to fabricate filters having sufficiently sharp cutoff and to match the optical carrier frequency and filter cutoff frequency with sufficient accuracy.
Multiple-subcarrier modulation (also called subcarrier multiplexing) represents a well-known approach to increasing the symbol interval. In this approach, the information bit stream is divided into multiple substreams at lower bit rates, and each substream is modulated onto an electrical subcarrier at a different subcarrier frequency. The modulated subcarriers are summed to form a frequency-division-multiplexed electrical signal, which is then modulated onto an optical carrier, usually by intensity modulation. While multiple-subcarrier modulation lengthens the interval of symbols transmitted on individual subcarriers, it does not necessarily reduce the total optical bandwidth of the transmitted signal. Multiple-subcarrier modulation offers poor average optical-power efficiency (e.g., compared to on-off keying, which is the same as 2-ary pulse-amplitude modulation), and this efficiency decreases further as the number of subcarriers is increased. Multiple-subcarrier modulation requires transmitters and receivers significantly more complicated than those required by baseband modulation techniques, such as on-off keying and M-ary pulse-amplitude modulation.
Modulation of information bits onto optical signals using M-ary phase-shift keying (for M≳3) or using M-ary quadrature-amplitude modulation (for M≳4) represent other well-known means to narrow the optical spectrum and lengthen the symbol interval of the transmitted signal. However, very complicated phase-sensitive detection techniques are required to recover the transmitted bits, such as synchronous homodyne or synchronous heterodyne detection.
It is well-known that M-ary pulse-amplitude modulation, in which information bits are encoded in one of M intensity levels during each symbol interval, where M≳3, represents a means to narrow the optical spectrum and lengthen the symbol interval as compared to on-off keying (which is equivalent to 2-ary pulse-amplitude modulation). It is well-known that for a given information bit rate, as M is increased, the spectrum narrows and the symbol interval increases. A key drawback of M-ary pulse-amplitude modulation is that for a given M, it does not offer the maximal spectral narrowing that can be achieved.
M-ary pulse-amplitude modulation with duobinary encoding is a well-known modulation technique that has been widely studied for a variety of communication media. For reasons to be described below, to date, only M=2 has been chosen in optical communication systems. In this technique, a sequence of M-ary pulse-amplitude modulation symbols, Im, where m is a time index of symbol intervals, is encoded to yield a duobinary symbol sequence Bm=Im+Im-1, which is transmitted. Duobinary encoding narrows the spectrum of the transmitted signal, and choosing M greater than 2 provides additional spectral narrowing and lengthens the symbol interval. A duobinary M-ary pulse-amplitude modulation signal takes on 2Mxe2x88x921 possible levels, including M-xe2x88x921 negative levels, Mxe2x88x921 positive levels, and zero. Optimal detection of duobinary M-ary pulse-amplitude modulation signals requires maximum-likelihood sequence detection, but at high bit rates, this is difficult to implement, so that symbol-by-symbol detection is typically performed, and the symbol sequence Im is precoded to avoid error propagation in the recovered information bits.
Numerous patents and research papers have documented the use of 2-ary pulse-amplitude modulation (which is equivalent to on-off keying) with duobinary encoding in optical communication systems. To our knowledge, all of these works have utilized precoding to permit symbol-by-symbol detection without error propagation. While these works have described many different techniques to implement precoding, duobinary encoding and modulation of the duobinary signal onto the optical carrier, all of these techniques result in transmission of equivalent optical signals, which take on one of three possible electric-field amplitude values, e.g., {xe2x88x92a,0, a}. Using precoded, 2-ary pulse-amplitude modulation with duobinary encoding, it is possible to recover the transmitted information bits by performing symbol-by-symbol detection on a signal proportional to the received optical intensity, such as the photocurrent in a direct-detection receiver. 2-ary pulse-amplitude modulation with duobinary encoding offers essentially the same average optical-power efficiency as on-off keying. While this technique narrows the optical spectrum by about a factor of two (as compared to on-off keying), it does not provide the narrowing that would be possible for M greater than 2, nor does it lengthen the symbol interval (as compared to on-off keying).
It is highly desirable to employ duobinary M-ary pulse-amplitude modulation, M  greater than 2, in optical communication systems, to achieve both a narrower optical spectrum and a longer symbol interval. However, with all previously known preceding techniques, it is not possible to recover the transmitted information bits using symbol-by-symbol detection on a signal proportional to the received optical intensity, such as the photocurrent in a direct-detection receiver, without potential error propagation. Using all previously known precoding techniques, for M greater than 2, it would be necessary to employ a complicated, phase-sensitive detection technique to receive the optical signal, e.g., synchronous homodyne or synchronous heterodyne detection. Hence, to date, it has not been possible to use duobinary M-ary pulse-amplitude modulation, for M greater than 2, in practical optical communication systems using direct-detection receivers.
There is a need for methods and apparatus to transmit and receive duobinary M-ary pulse-amplitude-modulated signals in optical communication systems, for any choice of M greater than 2, and for any choice of the M intensity levels, where the signals are precoded such that the transmitted information bits can be recovered using symbol-by-symbol detection on a signal proportional to the received optical intensity, e.g., by using a simple direct-detection receiver, without potential error propagation.
It is therefore an object of the present invention to provide methods and apparatus to transmit and receive duobinary M-ary pulse-amplitude-modulated optical signals, for M greater than 2, in optical communication systems.
Another object is to provide methods and apparatus to precode duobinary M-ary pulse-amplitude-modulated optical signals, for M greater than 2, such that the transmitted information bits can be recovered using symbol-by-symbol detection on a signal proportional to the received optical intensity, e.g., by using a simple direct-detection receiver, without the potential for error propagation.
Briefly, in a preferred embodiment of a duobinary M-ary pulse-amplitude modulation optical transmission system, information bits to be transmitted are formed into blocks of k bits, where k≲log2M. Blocks of k bits are input to a M-ary pulse-amplitude modulation symbol encoder, which encodes each block into a pulse-amplitude modulation symbol taking on one of M equally spaced levels, where M≳2. This encoding is performed using Gray coding. The encoder output is a M-ary pulse-amplitude modulation symbol sequence Dm, where m is a time index counting symbol intervals. When M greater than 2, the duration of each symbol interval is longer than the symbol interval using 2-ary pulse-amplitude modulation (which is equivalent to on-off keying).
The M-ary pulse-amplitude modulation symbol sequence Dm, is input to a precoder, which includes a multiplier, summer, one-symbol delay, polarity inverter and sign-computing device. The output of the precoder is a precoded pulse-amplitude modulation symbol sequence Im, which is related to the M-ary pulse-amplitude modulation symbol sequence Dm by:
Im=Dmsgn(Im-1)-Im-I. 
The precoded pulse-amplitude modulation symbol sequence Im has 2Mxe2x88x922 equally spaced levels. The purpose of precoding the symbol sequence is to allow the receiver to recover the transmitted information bits using symbol-by-symbol detection on a signal proportional to the received optical intensity, without potential error propagation. The precoded pulse-amplitude modulation symbol sequence Im is input to a duobinary filter, which uses a one-symbol delay and a summer to implement a delay-and-add function. The output of the duobinary filter is a duobinary, precoded symbol sequence Bm, which is related to the precoded pulse-amplitude modulation symbol sequence Im by:
Bm=Im+Im-1. 
The duobinary, precoded symbol sequence Bm has 2Mxe2x88x921 equally spaced levels. The purpose of duobinary filtering is to introduce temporal correlation into the symbol sequence, which narrows the optical spectrum of the transmitted optical signal by approximately a factor of two as compared to a M-ary pulse-amplitude modulation signal that has not been duobinary filtered. The duobinary, precoded symbol sequence Bm is input to a symbol remapper, whose output is another duobinary, precoded symbol sequence Bxe2x80x2m, which has 2M- l unequally spaced levels. The symbol remapper performs a one-to-one mapping of the 2Mxe2x88x92l levels taken on by the sequence Bm to a different set of 2Mxe2x88x921 levels taken on by the sequence Bxe2x80x2m. This remapping is performed because implementation of the precoder and duobinary filter is simplified if Dm, Im and Bm have equally spaced levels, but it is often desirable for Bxe2x80x2m to have unequally spaced levels. The duobinary, precoded symbol sequence Bxe2x80x2m is lowpass-filtered, resulting in the duobinary precoded pulse-amplitude modulation signal s(t), which has 2Mxe2x88x921 unequally spaced levels.
The duobinary precoded pulse-amplitude modulation signal s(t) is then modulated onto an optical carrier using a modulation subsystem. In the modulation subsystem, a laser or other light source generates an unmodulated optical carrier, which is input to a dual-drive, push-pull, Mach-Zehnder interferometric intensity modulator. The intensity modulator is driven by complementary drive signals V1(t)=Gs(t) and V2(t)=xe2x88x92Gs(t), each of which takes on values between xe2x88x92Vxcfx80/2 and Vxcfx80/2, where Vxcfx80 is the drive voltage required to produce a phase shift of xcfx80. The intensity modulator is biased by a d.c. bias chosen so that the modulator output is approximately zero when the drive signals V1(t) and V2(t) are zero. The modulator output is a duobinary M-ary pulse-amplitude-modulated optical signal described by the transmitted optical electric field Etrans(t), which has 2Mxe2x88x921 levels, including Mxe2x88x921 positive levels, Mxe2x88x921 negative levels (which are the negatives of the Mxe2x88x921 positive levels), and one level that is approximately zero. The transmitted optical electric field Etrans(t) is launched into the optical transmission medium, which may be a fiber or free-space optical medium.
At the output of the optical transmission medium, the received duobinary M-ary pulse-amplitude-modulated optical signal is described by the received optical electric field Erec(t). The transmitted information bits can be recovered from the received optical electric field Erec(t) using a direct-detection receiver, an asynchronous homodyne receiver, or an asynchronous heterodyne receiver. While each of these three receiver designs is implemented differently, each extracts from the received optical electric field Erec(t) a M-ary pulse-amplitude modulation signal v(t), which depends on Erec(t) only through the received optical intensity Irec(t)=|Erec(t)|2. Accordingly, the M-ary pulse-amplitude modulation signal v(t) has Mxe2x88x921 positive levels and one level that is approximately zero. The M-ary pulse-amplitude modulation signal v(t) is input to a M-ary pulse-amplitude modulation decision device, which performs M-ary symbol-by-symbol decisions by comparing the M-ary pulse-amplitude modulation signal v(t) to a set of Mxe2x88x921 thresholds. Because the M-ary pulse-amplitude modulation decision device does not perform decisions by comparing values of the M-level pulse-amplitude modulation signal v(t) in successive symbol intervals, decisions are not subject to error propagation. The M- ary pulse-amplitude modulation decision device yields at its output blocks of k recovered information bits, which are converted to a serial sequence of recovered information bits by a parallel-to-serial converter.
An advantage of the present invention is that the transmitted optical signal has a narrow optical spectrum, so that in wavelength-division-multiplexed systems, which utilize some form of optical or electrical filters to select the desired signal at the receiver, the spacing between carrier frequencies can be reduced subject to some constraints on the tolerable distortion to the desired signal caused by these filters and the tolerable crosstalk from undesired signals not rejected by these filters, thereby increasing the spectral efficiency of the system.
Another advantage of the present invention is that the transmitted optical signal has a narrow optical spectrum, reducing pulse spreading caused by chromatic dispersion in systems using single-mode fiber as the transmission medium.
Another advantage of the present invention is that the transmitted optical signal has a long symbol interval, improving the receiver""s ability to recover the transmitted information bits in the presence of dispersion (i.e., pulse spreading) originating from several sources, including chromatic dispersion or polarization-mode dispersion in single- mode fiber, modal dispersion in multi-mode fiber, and multipath propagation in free- space links.
Another advantage of the present invention is that the transmitted optical signal has a long symbol interval, reducing the electrical bandwidth required of electrical-to- optical converters, optical-to-electrical converters and electrical components in the transmitter and receiver.
Another advantage of the present invention is that the transmitted optical signal has a long symbol interval, reducing the clock speed required in the transmitter and receiver.
Another advantage of the present invention is that the transmitted information bits can be recovered using symbol-by-symbol detection on a signal proportional to the received optical intensity, such as the photocurrent in a direct-detection receiver.
These and other objects and advantages of the present invention will no doubt become obvious to those of ordinary skill in the art after having read the following detailed description of the preferred embodiments, which are illustrated in the various figures.